Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangles, or no triangle at all

Question

Solve each triangle that results. Include length of sides. a=11 , b=13, A= 57 degrees

thank you! :)

Answer 1

sinA / a = sinB / b

So, sin57° / 11 = sinB / 13

sinB = 0.9912

Sine is positive in quadrants 1 and 2, so there are 2 possibilities.

B = Sin^-1(0.9912) or 180° - Sin^-1(0.9912) = 82.4° or 97.6°

There are two triangles.